This paper draws on two studies of mathematics departments in 11-18 comprehensive maintained schools in England to compare and contrast the insights provided and questions raised by differing theoretical perspectives. In one study a mathematics department was viewed as a complex system and analysed accordingly. In the other activity theory was used to describe and analyse features of the departments involved. In both cases the departments involved were considered to be systems and it was the learning of the system rather than of individuals that was of interest. The affordances and limitations of the analytical perspectives are discussed
